Remark 2.1 The coefficients \(u_j(x)\)  in the definition of \(\Psi \)  are often required to be analytic functions near \(x=0\) , because the algebro-geometric constructions preserve this restriction; typically, statements of differential algebra hold formally, and in particular, our results are mostly concerned with polynomial coefficients, therefore we do not aim at complete generality. Analytic/formal cases of the ring \(\Psi \)  are treated in [1]}, with emphasis on certain types of modules over \(\Psi \) .

